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In this paper, the homotopy perturbation method will be applied to find the approximate solution of fractional order random ordinary differential equations, in which the fractional order derivatives and integrals are defined using Caputo and Riemann-Liouville definitions of fractional derivatives and integrals, respectively. Also, the convergence of the approximated solution is stated and proved in this work. The work is verified for three different examples, which are simulated for different generations of Brownian motion. [ABSTRACT FROM AUTHOR]

This paper deals with the effect of rotation on the onset of convection in magnetic nanofluids (MNF) with magnetic field dependent (MFD) viscosity using linear stability theory. As suggested by J. Buongiorno [1], Brownian motion and thermophoresis are important slip mechanisms in nanofluid. Since this work is based on MNF therefore, magnetophoresis is included as the third slip mechanism in addition to those mentioned above. Numerical method is employed along with MATLAB's EIG function to solve the resulting eigen value problem. Analysis is done graphically for ester-based MNF (EMNF) and water-based MNF (WMNF) through neutral stability curves (NSCs) and Critical stability curves (CSCs) for rigid-free boundary condition (Bcs) in gravity environment. The most significant parameter here is Taylor number (TA) which investigates the effect of rotation and the analysis shows that system gets stabilized with increase in the value of TA. [ABSTRACT FROM AUTHOR]

The combined effect of rotation and magnetic field dependent viscosity (MgFDV) in porous media on the onset of convection in magnetic nanofluids (MgN f) using linear stability theory is considered. The work embodies three important slip mechanisms:(a)Brownian motion (b)thermophoresis (both are suggested by J. Buongiorno in his work Convective Transport in Nanofluids, 2006), and (c) magnetophoresis, which is included due to the appearance of magnetic nanoparticles. We make use of the Chebyshev pseudospectral QZ-method for working on the derived eigen value problem and represent the result for water based magnetic nanofluidsWb-MgN f and ester based magnetic nanofluidsℇb-MgN f for free-free boundaries in the gravity envi-ronment. The results for various important parameters governing the flow such as Taylor number Ta, Lewis number Le, Langevin parameter αL are represented through neutral stability curves (NsCurves) and critical stability curves (CsCurves). It is observed that the two significant parameters of the problem viz., rotation and MgFDV both contibute in delaying the onset of convection. Also, Le, αL and Δφ assist in maintaining the stability of the system. [ABSTRACT FROM AUTHOR]

Gold is always outperformed other investments during economic recession. On top of that, gold mining industries is also highly depends on the world gold price in decision-making on mining projects. Thus it is crucial to forecast gold market price in future to help investors and mining sector in decision making. The aims of this study is to forecast the world gold market price for year 2022 using Geometric Brownian Motion (GBM) model and further to evaluate the suitability of the GBM model in forecasting during unexpected situations such as the Covid-19 epidemic. The accuracy of this model in forecasting world gold price been measured using Mean Absolute Percentage Error (MAPE). The gold price data set was collected from Yahoo Finance and composed of 1542 observations from 19th September 2016 to 19th September 2021. The MAPE value produced by GBM model were 12.21% which illustrates a good accurate. This indicate the GBM model able to forecast the world gold prices even during unexpected situation such as Covid-19. Lastly, the GBM model forecasting results shows an increasing trend for the world gold price in year 2022. [ABSTRACT FROM AUTHOR]

In this paper, steady two-dimensional magnetohydrodynamics mixed convective flow of non-Newtonian power-law nanofluid with the presence of heat generation/absorption and chemical reaction effects is investigated. The nanofluid incorporates the effects of Brownian motion and thermophoresis using Buongiorno's model. The flow is studied in a cavity with a moving top wall and contains isothermal solid circular cylinder at the center. The governing dimensional equations in a vector form are transformed into non-dimensional form. Then, the dimensionless equations are solved numerically by finite element method (FEM) using automated solution technique which is FEniCS. The influence of various parameters such as Richardson number, power-law index, magnetic field, heat generation/absorption, chemical reaction and size of solid circular cylinder on velocity, temperature, and concentration profiles are presented and discussed in this study. The results show that increasing Richardson number and power-law index has enhanced the velocity and the temperature profiles (left side of cavity). Meanwhile, both profiles reduce when the magnetic parameter and the size of solid circular cylinder are added. The temperature profile is increased with the rising of heat generation/absorption parameter. Besides that, declining trend is observed on the concentration profile with increasing chemical reaction parameter. [ABSTRACT FROM AUTHOR]

Numerous models have been proposed over time to study the behavior and properties of hybrid nanofluids. In this paper, a modified Buongiorno nanofluid model (MBNM) is used to investigate the stagnation-point flow of a hybrid nanofluid past a linearly stretching surface. The model combined Buongiorno's nanofluid model with Devi and Devi's hybrid nanofluid model. Compared to other models, it is still not widely used in the literature. It took into consideration the effect of Brownian motion and thermophoresis and the effective properties of the hybrid nanofluid. This paper also imposed the zero normal flux condition at the stretching surface instead of the usual constant nanoparticle concentration. The governing partial differential equations are transformed into ordinary differential equations using appropriate similarity variables. The problem is then solved numerically using the MATLAB function bvp4c. Results indicate that the stagnation parameter can significantly influence the magnitude of the skin friction coefficient. There is no skin friction when the surface moves at the same velocity as the fluid. The Brownian motion parameter is insignificant to both skin friction coefficient and the heat transfer rate of the fluid. It can also be seen that hybrid nanofluid indeed has a higher heat transfer rate as compared to mono-nanofluid. [ABSTRACT FROM AUTHOR]

A simulation of percutaneous drug absorption is given using the random walk method. The focus in the simulation is the diffusion process of the drug molecules from vehicle to stratum corneum membrane and then to blood vessels where the drug will be absorbed efficiently into the body. The diffusion process will be modelled as a Brownian random motion, where the diffusivity coefficients depend on the kinetical aspects of the drug molecules inside the vehicle and membrane. [ABSTRACT FROM AUTHOR]

Polymer electrolyte films have been reported to grow fractal patterns and simulations of these fractal patterns have been done. In this work, the Diffusion limited aggregation (DLA) model of fractal growth was integrated with Brownian motion theory in the computer simulations of fractal patterns in polymer electrolyte films via the application of fractal growth parameters. Growth rules along with major properties of the model were demonstrated. Computer simulation of the model applying fractal growth parameters extending their sticking coefficients, number of particles and lattice sites was performed on the Matlab platform. With the change in the growth parameters, noticeable differences in the simulation results were obtained. The fractal dimensions, D of the fractal patterns obtained from experimental and simulation work were calculated using the box-counting method. The effects of different growth parameters on fractal dimensions were also discussed here. [ABSTRACT FROM AUTHOR]

In this research, the significance of Hall and ion slip effect on the entropy generation and flow of Jeffrey nanofluid in an upstanding porous channel with the impact of suction/injection has been investigated. Thermal conductivity of the considered fluid is presumed to alter exponentially with temperature. This problem is mathematically formulated by using the Buongiorno's nanofluid model that describes the mass, momentum, energy and nanoparticle concentration conservation incorporating the Brownian movement and thermophoretic force impacts. Convective boundary constraints are imposed on temperature at the walls of the channel. The resulting governing equations are transformed into their non-dimensional system by defining suitable variables. The governing equations are solved by employing bvp4c MATLAB code. Velocity and temperature fields are analysed graphically for a scale of values of various physical variables. It can be reported from this study that velocity enhances while thermal field suppresses with the growing Hall and ion slip variables. Both velocity and thermal field enhances with the increment in Jeffrey parameter. Entropy generation in the flow can be minimized by increasing the porosity of the medium. [ABSTRACT FROM AUTHOR]

The study scrutinizes an MHD laminar boundary-layer Eyring Powell nanofluid flow across a wedge along with chemical reaction and Arrhenius activation energy. The convective boundary condition is takeninto account to model the process of heat transfer. Governing nonlinear PDEs have been converted into coupled, nonlinear ODEs by employing suitable similarity transformations. An obtained equation was numerically solved using bvp4c MATLAB code. An impact of various parameters such as Eyring Powell fluid parameters, magnetic parameter, wedge angle parameter, thermophoresis parameter, Schmidt number, Prandtl number, Brownian motion parameter, Reynolds number, dimensionless activation energy and Brinkman number along velocity, temperature, concentration and entropy generation fields are exhibited via graphs. Coefficient of skin friction, Nusselt and Sherwood numbers values are exhibited through tables. [ABSTRACT FROM AUTHOR]

This study investigates the magnetohydrodynamic Jeffrey nanofluid flow over an exponentially stretched sheet through a porous media with a constant boundary layer two-dimensional flow. Brownian motion, thermal radiation, and thermophoresis impacts on heat transmission must all be considered in the model, as well as nanoparticle concentration. Using similarity variables, guided partial differential flow relations are turned into ordinary differential systems. MATLAB bvp4c is used to solve these relationships numerically. The dimensionless momentum, heat measure, nanoparticle concentration, skin friction coefficient, rate of heat transfer, and rate of mass transfer numerical answers are tabulated and visually explained. Comparisons with previously published works are made in a number of special circumstances, and they are revealed to be in great agreement. [ABSTRACT FROM AUTHOR]

The Geometric Brownian Motion (GBM) model assumes that asset log returns are normally distributed. In fact, many asset log returns are found that are not normally distributed, therefore another model is needed, one of them is the Variance Gamma (VG) model. The VG process is a stochastic process. This process has three parameters which are generalizations of the Brownian motion that developed the Brownian. The added parameters are the drift of Brownian motion and the volatility of time changes. The VG process is used for modeling asset log returnsAs well as the GBM model, the VG model is widely applied in stock price modeling. Theoretically, the movement of the stock price of one company will be followed by the movement of the stock price of another company. Therefore, it would be more appropriate if the modeling was carried out together, namely using the Multivariate Variance Gamma (MVG) model. In this study, the Bivariate Variance Gamma (BVG) model was used. The data used is the daily closing price of stock of PT Bank Rakyat Indonesia (Persero) Tbk and PT Bank Negara Indonesia (Persero) Tbk. The parameter estimation was carried out using the maximum likelihood approach. Meanwhile, stock price prediction was carried out by using a Monte Carlo simulation approach. In this study, the prediction results using BVG obtained MAPE value less than10% which concludes that forecasting accuracy is excellent. [ABSTRACT FROM AUTHOR]

The aim of this research is to compare the stock price model of PT. Ciputra Development Tbk. i.e. between the ABM (Arithmetic Brownian Motion) model and the GBM (Geometric Brownian Motion) model. The measures of the goodness of the model are used MAPE (Mean Absolute Percentage Error), RMSE (Root Mean Square Error) and MAE (Mean Absolute Error). The data used is stock prices from August 11, 2020 to March 26, 2021 and is used to predict stock prices for the next 59 days, namely from March 29, 2021 to June 28, 2021. Simulation studies with repetitions of B=1000 times are used to calculate MAPE, RMSE and MAE and used to test whether the results are significantly different or not (with a level of significance α = 5%). The results obtained if the ABM model is used are MAPE = 19.60 %, RMSE = 238.84 and MAE = 200.96, while when GBM is used, they are MAPE = 24.23 %, RMSE = 293.86 and MAE = 249.27. The significant difference test (t.test) of the two results showed that the two results were significantly different. As a result, in this case the ABM model is more suitable to be used for the stock price data. This research can be developed for comparison of other stock price models such as the GBM model with jump. [ABSTRACT FROM AUTHOR]

The intension of the present research analysis is to explore by theoretical study about the flow of chemically reacting nanofluid above a stretched permeable sheet in rotation. The other effects combined are internal heat generation, activation energy and thermal radiation in a convective heat and mass transport of the system. The impacts of movement caused by Brownian action and thermophoresis which come about have been incorporated. On applying Runge-Kutta method numerical solution was obtained by coupling shooting technique. The study also reports the behaviour of all physical parameters on concentration, temperature and velocity through graphs. Local Sherwood and Nusselt numbers beside with skin friction coefficient are conversed quantitatively. Arithmetical results are tabulated. [ABSTRACT FROM AUTHOR]

We present the discontinuous Galerkin method applied to valuation of European options assuming that the underlying follows a CGMY process. This special case of an infinite activity Lévy process has purely discontinuous paths with finite and/or infinite variation with respect to the density of Lévy measure. The corresponding CGMY model was proposed as an extension of geometric Brownian motion to overcome some of the limitations of the Black-Scholes approach. The evolution of the option prices under this model can be expressed in the form of a partial integro-differential equation, which involves both integrals and derivatives of an unknown option value function. With a localization to a bounded spatial domain, the pricing equation is discretized by the discontinuous Galerkin method over a finite element mesh and it is integrated in temporal variable by a semi-implicit Euler scheme. The special attention is paid to the proper discretization of jump components. The whole procedure is accompanied with preliminary practical results compared to reference values. [ABSTRACT FROM AUTHOR]

In this work we consider time-fractional generalization of Black–Scholes equation, where assets follow a multidimensional geometric Brownian motion dynamics. The discretization of such models leads to linear systems with great computational complexity caused by the non-local nature of the fractional operator and the higher dimensionality. In this work, we develop Alternating Direction Implicit (ADI) method for solving these systems. We use graded time-space mesh in order to overcome the weak singularity of the solution at the initial time and non-smoothness of the pay-off. Numerical results are presented to illustrate the efficiency of the proposed ADI method. [ABSTRACT FROM AUTHOR]

Quantum random walks are the natural counterpart of the classical random walk, arising when quantum effects are taken into consideration. Many Monte Carlo methods use the classical Brownian motion as a building block. Although it appears naturally in various problems of computational physics, it is also used extensively in the stochastic models used for pricing of financial assets. When quantum random walks are used instead, more complex behaviors can be observed. However, the simulation of a quantum random walk requires more computational resources. By using low-discrepancy sequences instead of pseudorandom numbers, one may hope to decrease the statistical error of the simulation. Another approach for improved efficiency is to use the power of computational accelerators, which are suitable for problems, where a well-ordered sequence of computations is to be performed repeatedly. In our work we concentrated on using GPGPU computing in order to speed-up the operations involved in the generation of the low-discrepancy sequence as well as the subsequent sampling of the quantum random walks. In this work we explain our sampling algorithm and demonstrate its efficiency on model problems from the domain of option pricing. [ABSTRACT FROM AUTHOR]

The steady forced convective flow of a nanofluid boundary-layer over a stretching sheet in porous media with Newtonian heating and momentum slip effect is investigated numerically. The relevant partial differential equations are reduced into ordinary differential system by suitable transformations. The transport equations include the effects of Brownian motion and thermophoresis. Instead of the commonly used conditions of constant surface temperature or constant heat flux, a convective boundary condition is employed which makes this study unique and the results more realistic and practically useful. The features of the velocity, temperature and nanoparticle concentration distributions characteristics for different values of the governing parameters, namely, the magnetic field, Prandtl number, the Brownian motion, the thermophoresis, Lewis number, stretching/shrinking, first order momentum slip and Newtonian heating are analyzed and discussed in detail Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on velocity, thermal and concentration boundary-layers. The thickness of velocity boundary-layer decreases with an increase in the magnetic field and with a decrease in the first order slip parameter. Prandtl number and the first order slip parameter decrease the thickness of thermal boundary-layer and Brownian motion parameter, thermophoresis parameter, Newtonian heating parameter increase it. [ABSTRACT FROM AUTHOR]

In this study, we first discretize the fractional Brownian motion in time and observe multivariate Gaussian random variables (mGrv) to have a fractional Gaussian noise (fGn). Afterwards, we have discretized this discrete time process in space using a discretization proportion p and observe a random walk. We carry out this simulation study to foresee whether the correlated random walk using certain discretization parameters p behave similar to fBm. Based on this simulation study, we conclude on two important conjectures. First, there should exist a correlated random walk with parameter p converging to fBm since there exist correlated random walks behaving very similar to its originating fBm. Second, the convergence is satisfied for only certain values of p. [ABSTRACT FROM AUTHOR]

The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation. Moreover, the distribution of the time-changed Brownian motion by an inverse stable process solves the same equation, hence both processes have the same one dimensional distribution. In this paper we show the mutual singularity of the probability measures on the path space which are induced by generalized grey Brownian motion and the time-changed Brownian motion though they have the same one dimensional distribution. This singularity property propagates to the probability measures of the processes which are solutions to the stochastic differential equations driven by these processes. [ABSTRACT FROM AUTHOR]

In this article we present recent results in our ongoing study for weakly self-avoiding fractional processes leading to polymer models. In particular we sketch the results for stars and loops. For fractional random walks we give an explicit formula for the spring constants in the bead-spring model. Furthermore recent findings for the scaling properties of a weakly self-avoiding fractional Brownian motion are presented. [ABSTRACT FROM AUTHOR]

In occurrence of heat and mass fluxes, boundary-layer stable flow of a nanofluid through an exponentially porous shrinking surface is carried into regard. From this model, unified property of a thermophoresis and Brownian motion upon heat transfer with a nano-particle volume fraction is contemplated. A suitable similarity transformation is put on to get the equations then they are solved by using numerical technique shooting scheme R-K (Runge-Kutta) method of fourth order. The major effects are found by considering a variable mass and heat fluxes on temperature distribution and nano-particle volume fraction parameter. Rising a temperature distribution with enhance in Thermophoresis parameter and decelerates the concentration distribution while increase in Lewis number and Brownian motion parameter. [ABSTRACT FROM AUTHOR]

In this paper, a highly coherent laser is dispersed from a colloidal form of milk solution,an arbitrary grainy image named as speckle image is formed in observation plane due to Brownian motion. The outcomes shows that the statistical distribution of the intensity. The fluctuating nature of laser speckle in fluid medium is recorded for different concentration of the sample. Time progression of this interference image brings the required information of scattering particles.The aim of this work is the assessment of particle size by laser diffraction method through the dynamic speckle pattern. This laser scattering method helps to describe the corresponding speckle size for different concentration through image processing technique. [ABSTRACT FROM AUTHOR]

The present paper investigates the flow analysis of an incompressible Jeffrey fluid with nano particles in an inclined tube with overlapping stenosis. The solutions for velocity, wall shear stress, resistance to the flow have been derived by considering mild stenosis. It is observed that the resistance to the flow increases with stenosis height and also with Jeffrey fluid parameter and thermophoresis parameter, but it decreases with Brownian motion number, local nanoparticle Grashof number, local temperature Grashof number, and angle of inclination. It is also noticed that wall shear stress increases with Brownian motion number but decreases with thermophoresis parameter, Jeffrey fluid parameter, and inclination. [ABSTRACT FROM AUTHOR]

The intention of the current analysis is to examine mathematical model of blood flows through a tube with stenosis and dilatation under the influence of steady and incompressible micropolar fluid with nanoparticles. Coupled non-linear equations are solved by HPM method analytically. Effects of different physical parameters like micropolar parameter, coupling number, Brownian motion parameter, thermophoresis parameter, local temperature and nanoparticle Grashof number on flow resistance, shear stress at wall of the fluid are investigated. Effects of relevant parameters on arterial blood flow characteristics are studied through the graphs. It is seen that, the flow resistance enhances with the micropolar parameter, thermophoresis parameter, local temperature and nanoparticle Grashof number. But reduces with Brownian motion parameter and coupling number. [ABSTRACT FROM AUTHOR]

This paper numerically studied heat and mass transfer flow of Casson nanofluid near to the stagnation point due to the stretching sheet with the effects of viscous dissipation, space-dependent, and temperature-dependent heat source/sink. By using similarity transformations, the governing equations of the flow problem are converted into non-linear ordinary differential equations. The resulting obtained ODE'S are solved numerically by the Keller Box method. Analyzed the influence of various physical parameters on the velocity, temperature and concentration distributions shown graphically. Present results are compared with previously published work and results are found to be a very good agreement. The velocity profile decreases with an increase in the Casson parameter and magnetic parameter. Temperature profile increases with an increase in the Casson parameter, thermophoresis parameter, Brownian motion parameter, Eckert number, space dependent internal heat source/sink, and temperature-dependent internal heat source/ sink parameters increase, while a decrease in Prandtl number. Concentration profile increases with increase Casson parameter and thermophoresis parameter. [ABSTRACT FROM AUTHOR]

A laminar magnetohydrodynamic (MHD) forced convection two phase nanofluid model in porous medium is considered along with Marangoni convection. It is assumed that the surface tension varies linearly with both the temperature and concentration and that the interface temperature and concentration are quadratic functions of the interface arc length x. Numerical solutions for the velocity, temperature and concentration distributions are obtained by using Shooting method. Influences of the Marangoni ratio, Schmidt number, Brownian motion parameter, magnetic number and thermophoretic parameter on the hydrothermal characteristics are presented through graphs and tables. Results depict that the temperature increases with increase of Permeability of porous medium, the Schmidt number, Brownian motion, magnetic number and the thermophoretic parameters but it reduces with the rise of the Marangoni ratio. [ABSTRACT FROM AUTHOR]

The Stock is defined as an investor ownership sign of their investment or the amount of fund invested in a company. In the transaction process of stock exchange, stock is the most instrument traded. Thus, the forecasting of stock price is very important to develop an effective market trading strategy. The forecasting of stock prices can anticipate investment losses and provide optimal benefits for investors. In this paper, Microsoft stock prices will be predicted by the geometric Brownian motion and multilayer perceptron methods. Prediction of stock prices using geometric Brownian motion was begun by calculating the return value of the data. Then, the normality test of the return value is carried out. The value of return must be normally distributed. Then, we do calculation to get the value of drift and volatility. The parameters of geometric Brownian motion are assumed constant. The parameter values will be used as input in prediction process with MATLAB. In the multilayer perceptron method prediction, the data divided into two parts, 70 % for training data and 30 % for validation data. Then, the data must be normalized first. In the prediction process using multilayer perceptron, we will initialize the weight, correct the weight values, correct bias and calculate error value. As the result, the MAPE value from multilayer perceptron method predictions was 0.05266. This value obtained when the number of neurons are 2 in the input and the number of neurons are 3 in the hidden layer. Meanwhile, the MAPE value produced by geometric Brownian motion method were 0.0221 when 10 trajectories and 0.019571689 when 10000 trajectories. Then, the result of geometric Brownian motion method is better than multilayer perceptron method. [ABSTRACT FROM AUTHOR]

The article considers some generalizations of the classical Black-Scholes models in finance, based on Lévy processes, additive processes and Grigellionis processes. All this processes can be considered as generalizations of the Brownian motion. Also, an alternative of Brownian motion is considered – telegraph processes – which may be used to describe process of financial instruments. A proposal for generalization of telegraph processes is made based on ST-processes. [ABSTRACT FROM AUTHOR]

The unsteady free convection flow of a non-homogeneous nanofluid over a uniformly moving vertical plate is investigated. The two imperative parameters associated with nanoparticle-based fluid mixture i.e. thermophoresis and Brownian motion effects are considered by applying Buongiorno’s model with passively controlled nanoparticle concentration at the boundary. The nonlinear partial differential equations are reduced to dimensionless forms and then numerically solved using the Crank-Nicolson method. The impact of time, thermophoresis and Brownian motion on nanofluid velocity, temperature, nanoparticle concentration, local and average Nusselt numbers and skin-friction are investigated and presented. The Nusselt number is found to be enhanced with the increase of Brownian motion parameter. However, the opposite trends are observed for the thermophoresis parameter. The average skin-friction is found to be increasing with an increase in Brownian motion parameter. The present local Nusselt numbers for limiting case at different Prandtl numbers are observed to be in good agreement with the pure fluid correlation results, which verifies the accuracy of the numerical scheme. [ABSTRACT FROM AUTHOR]

In this study thermophoresis and Brownian motion effects on natural convection in an enclosure with an adiabatic obstacle filled with Cu-water nanofluid is investigated. The Navier Stokes equations in their vorticity-stream function form are used to simulate the flow pattern, isotherms and concentration. The governing equations are solved via Galerkin’s Finite Element Method. Effect of Lewis number (Le = 2,4,6 and 8) on streamline, isotherm, iso-concentration and local Nusselt numbers are examined. The results indicate that Nusselt number is a decreasing function of Lewis number. [ABSTRACT FROM AUTHOR]

In this research photothermal energy conversion in nanofluids was numerically studied using a CFD model. A Direct Absorption Collector (DAC) of cylindrical shape with incident light on one of its surfaces was adopted for the simulations. The Eulerian two-phase transient model included the volumetric absorption of light, losses to the surroundings and the Brownian motion. The simulation results were validated with experimental data, demonstrating modest discrepancies. The model was studied parametrically, altering particle volume fraction, collector height and surface transparency. We found that: the efficiency drops by 43% when the absorber height is reduced from 7.5 to 1.0 cm; the maximum efficiency was 67% at 50 ppm (1 cm absorber) of the nanoparticles; the efficiency of the DAC with nanofluid is 20% greater than the efficiency for the surface absorber; natural convection in the collector improves the efficiency by 7%. [ABSTRACT FROM AUTHOR]

We present here, a procedure for developing the hydrodynamic description of a system of active particles starting from microscopic equations of motion. The microscopic dynamics of an individual active particle is described as a Brownian motion having a noise term and momentum dependent frictional coefficients describing the surrounding drag. The single particle dynamics is first used to obtain balance equations for corresponding collective densities. We average the time evolution equation for collective densities over local equilibrium distribution to obtain the hydrodynamic equations in terms of coarse-grained density fields. The macroscopic equation obtained contains multiplicative noise originating from the additive noise in the equation of motion for the active Brownian particle. The parameters of the macroscopic equations are obtained in terms of the microscopic description of the active Brownian system. [ABSTRACT FROM AUTHOR]

Dynamics in nano domain is different from that of macro domain. Forces which are considered weak in macro world like Van der Waals, electrostatic interactions, Brownian are seen playing significant role in the motion of particle at nanoscale. The importance of stiffness in Brownian motion for a nanoparticle had been established and published in literature. It is observed that when a particle has low stiffness it tends to behave differently from its stiffer counterparts. Present work investigates the significance of near zero value of stiffness on variance in motion of nanoparticle with the help of simulations in MATLAB. Brownian motion of the nanoparticle is modeled using langevin equation considering non-rigidity of matter. [ABSTRACT FROM AUTHOR]

The apparent complex viscosity of a non-Brownian Newtonian concentrated suspension is known to be a nonmonotonic function of the applied strain, attaining a minimum at a relative strain of about 100%. This behaviour can be nicely described in the framework of the Stokesian dynamics, which also predicts the independence of the complex viscosity on the applied frequency. Despite this, recently it was experimentally shown that the apparent viscosity of a concentrated non-Brownian suspension is function of the applied frequency in experiments run imposing a constant stress (Carotenuto et al. AIP Conference Proceedings 1599, 258, 2014). This behaviour is quite unexpected and we here confirm it in more canonical experiments run imposing a constant strain. [ABSTRACT FROM AUTHOR]

We study a stochastic differential equation with rank-based characteristics on the plane. We find its flow solutions and characterize coalescence. [ABSTRACT FROM AUTHOR]

Let 0 < α < 1, b, T be positive real numbers, Lαu = ut - (…), where … denotes the Riemann-Liouville fractional derivative. This paper consider the problem Lαu(x, t) = δ(x - b)f(u(x, t)) in (-∞,∞) x (0, T], subject to initial and boundaries condition {u(x, 0) = φ(x) in (-∞, ∞), with φ (x) → as |x| → to u(x, t) → 0 for 0 < t ≤ T, as |x| → ∞, where δ(x - b) is the Dirac delta function, f and φ are given functions. We assume that φ ≥ 0, f (0) ≥ 0, f'(u) > 0, f"(u) > 0 for u > 0. By using Green's function, the problem is converted into an integral equation. It is shown that there exists tb such that for 0 ≤ t ≤ tb, the integral equation has a unique nonnegative continuous solution u; if tb is finite, then u is unbounded in [0, tb). Then, u is proved to be the solution of the original problem. [ABSTRACT FROM AUTHOR]

The onset of oscillatory magnetoconvection for an infinite horizontal nanofluid layer subjected to Soret effect and internal heat source heated from below is examined theoretically with the implementation of linear stability theory. Two important properties that are thermophoresis and Brownian motion are included in the model and three types of lower-upper bounding systems of the model: rigid-rigid, rigid-free as well as free-free boundaries are examined. Eigenvalue equations are gained from a normal mode analysis and executed using Galerkin technique. Magnetic field effect, internal heat source effect, Soret effect and other nanofluid parameters on the oscillatory convection are presented graphically. For oscillatory mode, it is found that the effect of internal heat source is quite significant for small values of the non-dimensional parameter and elevating the internal heat source speed up the onset of convection. Meanwhile, the increasing of the strength of magnetic field in a nanofluid layer reduced the rate of thermal instability and sustain the stabilization of the system. For the Soret effect, the onset of convection in the system is accelerated when the values of the Soret effect is increased. [ABSTRACT FROM AUTHOR]

Magnetic field in Marangoni thermal instability in an infinite parallel plane of nanofluid layer together with internal heat source is investigated using linear stability theory. Two important properties of thermophoresis and Brownian motion are included in the model and two types of lower free-upper free and lower rigid-upper free bounding systems of the model are considered. The system is assumed to be heated from below and the eigenvalue equations are gained from a normal mode analysis and executed numerically by using Galerkin technique. Influences of magnetic field within nanofluid layer always stabilize the system and the initiation of thermocapillary instability in an infinite parallel plane of nanofluid layer gets advanced with the increased in internal heat source. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of a passive probe particle in a bath of active granular chains (AGC). The bath and the probe are enclosed in an experimental compartment with a sinusoidal boundary to prevent AGC congestion along the boundary while connected to an electrodynamic shaker. Single AGC trajectory analysis reveals a persistent type of motion compared to a purely Brownian motion as seen in its mean squared displacement (MSD). It was found that at small concentration, ϕ ≤ 0.44, the MSD exhibits two dynamical regimes characterized by two different scaling exponents. For small time scales, the dynamics is superdiffusive (1.32-1.63) with the MSD scaling exponent increasing monotonically with increasing AGC concentration. On the other hand, at long time, we recover the Brownian dynamics regime, MSD = DΔt, where the mobility D ∝ ϕ. We quantify the probe dynamics at short time scale by modeling it as a fractional Brownian motion. The analytical form of the MSD agrees with experimental results. [ABSTRACT FROM AUTHOR]

Time-dependent diffusion coefficients arise from anomalous diffusion encountered in many physical systems such as protein transport in cells. We compare these coefficients with those arising from analysis of stochastic processes with memory that go beyond fractional Brownian motion. Facilitated by the Hida white noise functional integral approach, diffusion propagators or probability density functions (pdf) are obtained and shown to be solutions of modified diffusion equations with time-dependent diffusion coefficients. This should be useful in the study of complex transport processes. [ABSTRACT FROM AUTHOR]

The present study is performed to investigate the effect of unsteadiness, stretching ratio, Brownian motion, thermophoresis and magnetic parameter on boundary layer such as momentum, thermal and nanoparticle concentration. In this respect we have considered the magnetohydrodynamic (MHD) unsteady boundary layer nanofluid flow and heat - mass transfer over a stretching surface. The dimensionless governing equations are unsteady, two-dimensional coupled and non-linear ordinary differential equations. The numerical solution is taken by applying the Nachtsgeim-Swigert shooting iteration technique along with Runge-Kutta integration scheme. The effects of various dimensionless parameters on velocity, temperature and nanoparticle concentration are discussed numerically and shown graphically. Therefore, from the figures it is observed that the results of velocity profile increases for increasing values of magnetic parameter and unsteadiness parameter but decreases for stretching ratio parameter, the temperature profile decreases in presence of Brownian motion, unsteadiness parameter, stretching ratio parameter and thermophoresis parameter but increases for magnetic parameter and, the nanoparticle concentration decreases for increasing values of thermophoresis parameter, unsteadiness parameter and stretching ratio parameter whereas the reverse trend arises for Brownian motion & magnetic parameter. For validity and accuracy the present results are compared with previously published work and found good agreement. [ABSTRACT FROM AUTHOR]

The onset of double diffusive convection in a horizontal layer of a porous medium saturated with an Oldroyd nanofluid is studied using linear and non-linear stability analysis. The modified Darcy- Oldroyd model is used for the momentum equation. The model used for the Oldroyd nanofluid incorporates the effects of Brownian motion and thermophoresis. The thermal energy equations include the diffusion and cross diffusion terms. The linear theory depends on normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The effects of various governing parameters viz., concentration Rayleigh number, nanofluid Lewis number, modified diffusivity ratio, Soret and Dufour parameters, Solutal Rayleigh number, Vadasz number, Lewis number, relaxation, and retardation parameters, viscosity ratio and conductivity ratio on the stationary and oscillatory convections are presented graphically. The non-linear theory based on the representation of Fourier series method is used to find the heat and mass transport. The effect of various parameters on transient heat and mass transfer is also brought out and nonlinear analysis depends on a minimal representation of double Fourier series. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large all the three transient Nusselt values approaches to their steady state values. [ABSTRACT FROM AUTHOR]

We present estimators of the dimension of the support of a probability distribution. These estimators are derived from the concept of quantization dimension. For the general case consistency results are discussed. Versions of the estimators may be applied for instance to estimate the dimension of the driving Brownian motion of Itô processes. [ABSTRACT FROM AUTHOR]

A new empirical expression for a decay half lives is proposed by generalizing the Brown formula. The involved parameters are fixed through two fitting schemes performed on the available measured data regarding the α decay Qα values and half lives for 96 superheavy nuclei. The two fitting procedures allow the comparison of the newly proposed formula with the Viola-Seaborg and Royer formulas, which reveals a superior predictive power of the former. Exploiting the similarly excellent agreement with experimental data obtained with all fitting formulas, one generated α decay predictions for 125 unknown superheavy α emitters. The comparison of the data predicted by the different fitting formulas shows a high degree of superposition in a number of 36 nuclei whose average half-live values are considered as highly probable in what concerns experimental realization. [ABSTRACT FROM AUTHOR]

The physical setting in which a charged particle undergoes Brownian motion in a magnetic field is studied and the results are discussed in an astrophysical context. The mathematical description associated to this physical setting is based on Langevin equations. These are solved numerically, for both thermal and explosive initial conditions. Special attention is devoted to the Light Curve generated during the motion, its statistical moments and its Power Spectral Density. [ABSTRACT FROM AUTHOR]

We present estimators of the dimension of the support of a probability distribution. These estimators are derived from the concept of quantization dimension. For the general case consistency results are discussed. Versions of the estimators may be applied for instance to estimate the dimension of the driving Brownian motion of Itô processes. [ABSTRACT FROM AUTHOR]

In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model, in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown in Christoffersen, Heston and Jacobs [12].We consider one modified form of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this paper is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. [5, 6]. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi [11] using method of characteristics, Fourier and bivariate Laplace transforms. [ABSTRACT FROM AUTHOR]

The stochastic Brownian particle-kinetics in a superparamagnetic ferrofluid at room temperature is of significance in nullifying total magnetization vectors of the suspended particles. Correspondingly, the apparent magnetization response observed under static magnetic field shows no hysteresis loop, but being linear at a given finite field-difference. Owing to this superparamagnetism, we propose a differential magnetometry to analyze the static fieldinduced particle-kinetics and further to identify the effective field-strength in reorienting particle-moments toward the applied field direction. A polydispersive ferrofluid containing iron-oxide nanoparticles, in practice, is subjected to a verylow oscillatory-field, immediately after applying the static-field. For a given frequency, we confirm a decreasing ac susceptibility as dc field-strength increases, which suggests a statistically less fluctuating magnetization-vectors. Via numerical integration of ac susceptibility recorded, we furthermore estimate the nonlinear quasi-static magnetization at various measurement frequencies. The resulting nonlinearity is attributable to the contributing relaxation dynamics of the particles. More importantly, the difference between dc and ac susceptibilities is found to be field-strength and frequencydependent. Its value is further maximized at an effective field-strength, from which we identified the coexisting energybarriers. [ABSTRACT FROM AUTHOR]

This paper deals with the valuation of options in markets without liquidity and under stress. More precisely, a European option is considered when the underlying asset’s dynamic is governed by a Brownian motion. Following Liu and Yong [1], a term related to the number of invested stock is embedded into the model. Moreover, the volatility of the asset is augmented by a separate function that models the abnormal increase of the volatility. Under these settings, we deal with the evaluation of European options. [ABSTRACT FROM AUTHOR]